2011 ece 227a homework solution #1 chapter 1
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2011 ECE 227A Homework Solution #1
7. In practice, there are two general nonradiative mechanisms for carriers that are
important. The first involves nonradiative recombination centers, such as point defects,
surfaces, and interfaces, in the active region of the laser. To be effective, these do not
require the simultaneous existence of electrons and holes or other particles. Thus, the
recombination rate via this path tends to be directly proportional to the carrier density, N.
The second mechanism is Auger recombination, in which the electron–hole
recombination energy, E21, is given to another electron or hole in the form of kinetic
energy.
Thus, again for undoped active regions in which the electron and hole densities are equal,
Auger recombination tends to be proportional to N3 because we must simultaneously
have the recombining electron–hole pair and the third particle that receives the ionization
energy.
9. In direct bandgap double heterostructures, carriers are confined inside the PIN
junction, and most of them recombine inside the I region, in transit between P and N. In a
regular PN diode, very few carriers recombine in the junction, and they are just swept
across the junction by the electric field.
2011 ECE227A Homework #2 Solutions
11.
i) bulk material is normally thicker than quantum wells.
ii) For quantum wells, carriers are confined in the wells, so the carrier injection
efficiency is higher.
iii) The density of states are different. Quantum wells have separate energy states,
while the energy states of bulk material are quasi-continuous.
12.
i) They need to lattice matched to avoid a lot of defects.
ii) The cladding material must have a larger bandgap and smaller refraction index
at working wavelength, compared to the waveguide material.
13.
i) Si has an indirect bandgap, and most of the III-V materials, such as GaN, InP,
GaAs, have direct bandgap. For indirect bandgap material, phonons are generally
needed to generate photons because of the different crystal momentum between
conduction band valance band. So their efficiency to generate light is very low.
14. GaAs/AlGaAs – datacom lasers in the ~700-900nm range, a lot of them vertical cavity.
InGaAsP – in-plane lasers for telecom and sensing, 1.3-1.6um.
15. The main material parameter controlling the current leakage in a double heterostructure or a
quantum well is the conduction band offset. The band offset will determine the height of a
quantum well in a laser active region. Due to their much lighter effective mass, electrons require
much tighter confinement with increasing temperature than holes. Thus, it is important to have
high band offset in the conduction band. For GaAs/AlGaAs, 2/3 in the conduction band, for
InP/InGaAsP, 40% in the conduction band.
16.
17.
18.
20 wells, because of the energy states splitting. ( Assuming the wave function of
the first well can still affect the 10th well.)
19.
Since the electrons in InGaAsP material has quite high mobility and they tend to
escape from the quantum at high temperature, decreasing the injection efficiency.
To improve the performance of laser at higher temperature, the electron leakage
current can be decreased by increasing the conduction band offset.
20. Blue laser has lower wavelength than the red laser – thus, the minimum spot size that
can be resolved on a Blu ray disc is smaller than that of a regular DVD. To get an even
higher capacity, we should use an ultra violet laser.
21. Aixtron and Veeco.
23. When interpolating, one must be careful if different bands come into play in the
process as discussed in the text. For this case, InAlSb's bandgap changes from direct to
indirect for x = 0.535. The plot is shown below.
